Ramm, A. G. Analytical solution of a new class of integral equations. (English) Zbl 1034.45001 Differ. Integral Equ. 16, No. 2, 231-240 (2003). The author gives an algorithm for finding analytically the unique solution \(h\in H^{-\alpha}(0,L)\) to the following equation \(Rh= f\), where \(Rh= \int^L_0 R(x,y) h(y)\,dy\), and the kernel \(R(x,y)\) satisfies the equation \(QR= P\delta(x-y)\), \(0\leq x\leq L\). The above equation is the basic equation of random processes estimation theory. Finally, generalizations of the above equation in the multidimensional case are also considered. Reviewer: Rashmi Jain (Jaipur) MSC: 45A05 Linear integral equations 45H05 Integral equations with miscellaneous special kernels 60G60 Random fields 93E10 Estimation and detection in stochastic control theory Keywords:integral equations; estimation and detection; random processes; analytical solution × Cite Format Result Cite Review PDF Full Text: arXiv